You are asking for something similar to "What's the lore of Europe" btw.
What about characters?
Who are the Aragorns and Morgoths and Zeus' in this world or at least in the Forgotten Realms campaign setting?
Who are the main human factions for instance?
I'll second what Mich has said. Perhaps a better comparison would be asking what's the lore of fantasy novels. There is no one world, no one setting, no one set of characters.
Even if you limit yourself just to the Forgotten Realms universe, you have to ask which continent, which region, which people, which time period. There is no single story with just a dozen main characters of any importance, like you might find in LOTR or King Arthur.
As others have explained, D&D is NOT a single region, or world, or universe. D&D is a rule system by which you can make your own world and story. Most stories have centered on standard medieval fantasy settings, but there are plenty of others, such as asian settings, african, desert planets, space travel, fantasy worlds with a race of sentient [s]robots[/s] golems... D&D is just the rules framework for whatever setting you want. IIRC Kotor 1 used the D&D rules (D20)... would D&D lore include that, or would it be considered star wars lore?
You really have to narrow your question down to get a meaningful response. "What's the lore of D&D" is both impossibly broad and also nonsensical. If you're asking about a specific video game, like BG or NWN, I think you'd get a much better response saying so.
In a nutshell, FR has hundreds of gods spread over dozens of pantheons. Each god has a few mortals given major blessings, called "Chosen of _________". Elminster for example, is a Chosen of Mystra, human goddess of magic. Being a Chosen basically makes you a rules-breaking overpowered munchkin mary sue. At one point all the gods were stripped of most of their power and cast down amongst the mortals by Ao the Overgod. This was called the Time of Troubles. A few gods died, but eventually Ao let all the gods return, and it's right after this time that BG is set (Bhaal, god of murder, was one of the gods who died).
[url=http://forgottenrealms.wikia.com/wiki/Portal:Deities]List of some FR gods, scroll down, left hand side[/url]
Most of the areas where gameplay occurs in FR has moved from feudal kingdoms to city-states. The cities of Neverwinter and Baldur's Gate are both city-states. Humans are the vast majority, as elves have withdrawn across the ocean, dwarves are underground, and gnomes and halflings live far, far to the south.
There are some large factions in FR, the Harpers and Zhentarim mentioned in those two games. Basically, the Harpers are a secretive group of "good" guys, while the Zhents are a secretive group of "bad" guys. Jaheira and Khalid are Harpers, Elminster is one of the leaders (finger in every pot), while Xzar and Monty are Zhents. summary of some FR factions